Characteristics Of A One-dimensional Periodic And Aperiodic Crystals Phonon Band

It is a fresh field that the phononic crystal has been developed for several decades, which is still the stage of fundamental theory. According to the known research results, the vibration performance of the acoustic wave in the phononic crystal has been demonstrated, and then the energy fundamental characteristic of the acoustic wave has been displayed.Based on the standard transfer matrix method and the local mode of vibration in solid state physics, the design methods for macroscopic apparatus with having molecule-like energy states by using two-component ultrasonic phononic crystal with alternate layers of plexiglas and water cavities have been theoretically discussed. The well pronounced acoustic Wannier-Stark Ladder and Bloch oscillations appearing in the transmission spectra of phononic crystal with water cavities of a given gradient of thicknesses have been demonstrated. The acoustic wave dynamic evolvement in the stop-band edge is investigated theoretically and experimentally by using the acoustic cavity made of two identical acoustic phononic crystal. The theoretical and experimental results show that the acoustic waves are periodic oscillations with the increase of the acoustic cavity, and the tunneling effect of the acoustic wave is easier in the in stop-band edge of phononic crystal. And, the resonant tunneling effect of the transmitted acoustic wave in the tunable resonant cavity composed of two identical one-dimensional acoustic phononic crystal has been reported. The resonant tunneling process is similar to the resonant tunneling effect in Quantum Mechanics. By adjusting the length of acoustic resonant cavity, the dynamic evolvement of the acoustic wave in the stop-band edge of phononic crystals is displayed. The experiment results show that, the transmitted acoustic wave periodically moves towards the stop-band region with the increase of the resonant cavity length. The localized vibrational modes in a phononic crystal with a cavity layer have been studied theoretically, and the simple formulas for the eigenfrequency of this localized mode and the corresponding decay factor has been derived. These above results indicate that phononic crystal composed of macroscopic-size materials manifest similar microphysics effects, which is of scientific significance to make more practical superlattice apparatus by macroscopic-size materials. Finally, the localized vibrational modes in a superlattice with a defect layer have been theoretically studied. In particular, the simple formulas for the eigenfrequency of this localized mode and the corresponding decay factor have been derived, of which show explicitly how these quantities depend on the constituent layers of the superlattice and also the width of the defect layer. These formulas are useful for systematic understanding of the localized acoustic phonons in superlattice.This paper is organized as follows:Section I briefly introduces the basic concepts with fundamental theory, and elaborates the physical principles of the generation of energy bands and the formation of wave packet. Section II mainly describes the properties of resonant tunneling effect in phononic crystals, the transmitted acoustic wave periodically moves towards the stop-band region with the increase of the resonant cavity length. Section III demonstrates the dynamic characteristic of one-dimensional aperiodical phononic superlattices, and the macroscopic-size apparatus manifests analogous microphysics effects. Section IV theoretically studies the localized vibrational modes in a superlattice with a cavity layer, which is useful for systematic understanding of the localized acoustic phonons in superlattice. Section V discusses prospects for further work and the possible application of the described novel acoustic devices for the manipulation of the way in which acoustic phonons interact with other phonons, with electrons, and with light.